// Description of sigma(W) and f_W for the Coxeter group:
Coxeter group: Finitely presented group on 4 generators
Relations
    s * t * s = t * s * t
    s * u = u * s
    s * v = v * s
    t * u * t = u * t * u
    t * v * t = v * t * v
    u * v = v * u
    s^2 = Id($)
    t^2 = Id($)
    u^2 = Id($)
    v^2 = Id($)


// W has order 192.


// 7 elements of W do not lie in \sigma(W).
// They are:

c := [ 
t * v * t * s * u * t * v,
t * u * t * s * v * t * u,
s * u * t * v * t * s * u,
t * s * u * t * v * t * s * u,
s * u * t * v * t * s * u * t,
t * s * u * t * v * t * s * u * t,
s * t * s * u * v * t * s 
 ];


 // Values of f_W on the above elements (critical sets):

 p := [ 
[ t * v * t * s * u * t * v , t * v * t  ],
[ t * u * t * s * v * t * u , t * u * t  ],
[ s * u * t * v * t * s * u , s * u * v  ],
[ t * s * u * t * v * t * s * u , t * s * u * v  ],
[ s * u * t * v * t * s * u * t , s * u * v * t  ],
[ t * s * u * t * v * t * s * u * t , t * s * u * v * t  ],
[ s * t * s * u * v * t * s , s * t * s  ],
 ];